(a) Schematic of four nodes separated into a unidirectional ring. (b) Experimental setup for a single node, an optoelectronic, nonlinear oscillator, with time-delayed feedback.
Representative time traces for four different values of the coupling delay, each displaying a different phase relationship between the four nodes, as denoted by δ k , the phase shift between successive oscillators in state Sk . Experimental traces are on the left; simulations are on the right.
Master stability function, or maximum Lyapunov exponent (MLE), of four different synchronization states: δ0 = 0 (isochronal synchrony), δ1 = π/2 or δ3 = 3π/2 (splay-phase synchrony), and δ2 = π (cluster synchrony). A negative MLE indicates the stability of a particular phase relationship. (a) MLE as a function of coupling delay τ c calculated over a wide range of delays. (b) Enlargement of (a) for narrow range of τ c .
The phase relationships present as a function of coupling delay. For each coupling delay τ c , the percentage of different random initial conditions resulting in a particular phase relationship δ is shown by the grayscale. The top figure shows the experimental results, with 10 different initial conditions for each delay. The bottom figure shows the simulations results, with 2000 different initial conditions for each delay.
Multistability between synchronization states for long coupling delays, as observed for 50 different random initial conditions in simulations.
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